Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26012502 | C2 | semidirect |
| 3. #26012501 | C2 | semidirect |
| 12. #19149748 | C22 | semidirect |
| 13. #19149747 | C22 | semidirect |
| 15. C2×#14583810 | C4 | semidirect |
| 16. C2×#14583809 | C4 | semidirect |
| 17. M16×D173 | C4 | semidirect |
| 20. C2×M16×C173 | C4 | semidirect |
| 38. #14583810 | C2×C4 | semidirect |
| 39. #14583809 | C2×C4 | semidirect |
| 40. C2×#13063436 | C2×C4 | semidirect |
| 41. C8×D173 | C2×C4 | semidirect |
| 44. M16×C173 | C2×C4 | semidirect |
| 45. C2×C8×C173 | C2×C4 | semidirect |
| 97. C173 | #2911 | semidirect |
| 108. C2×M16 | #10621924 | semidirect |
| 133. M16 | C2×#10621924 | semidirect |
| 137. C2×C8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| #26012502 | 2 |
| #26012501 | 2 |
| C2×M16×D173 | 2 |
| #2911 | 173 |